can I use the background as attached ? 

Also there is a four-volume book about TEM is written by David B. Williams and C. barry Carter. You can find the answer in .

Just Kidding Mate :)

Good Luck.

Your curve fit (which I presume is a power-law extraction) doesn't look too bad, but it's not great either. I have a few questions:

-The fit suddenly starts getting worse at about 8/nm. Is there anything clearly happening at this point in the 2D image that this came from? Is that, perhaps, the distance from the center of the pattern to the nearest point on the edge? Or is there perhaps an amorphous support layer with a diffuse peak cutting off at about this point? If there's a plausible reason why the fit should suddenly start to fail at that point, then suddenly your result becomes a lot more believable. If there is a strong substrate contribution, then you should do a separate measurement of just the substrate without your sample on it, and align and subtract that (possibly times a scalar multiple to account for multiple scattering and different instrument conditions for different acquisitions).

-It's important to establish the precision to which you can extract the background. It's hard to do this rigorously, but one thing you can do is see how much the integrated background-subtracted peak intensity numbers change when you vary parameters that, you would hope, wouldn't change the answer. Like the positions of the left and right edges of the range used for fitting the background, for example. Or the functional form of the background. There's a judgment call here, though. You're basically determining how much the answer changes over the range of all background fits that "look good." Since you have no objective, quantitative measure of "looking good," you can pretty much just get an estimate of the precision but not a hard number. Still, it's very much worth going through this procedure. If you find that any reasonable-looking background model gives you the same answer to within 5%, then you can have reasonable confidence in your values at roughly the +/- 5% level, for example. Error analysis isn't always exact.

-How well did the center-finding algorithm work? The performance of rotational averaging is critically dependent on the precision with which the center of the pattern can be determined. If small changes in the pattern-center x and y parameters have a significant effect on the sharpness of the peaks, then this needs to be considered.

-As you can see, the signal-to-background ratio that you calculate for a peak will depend strongly on where you choose to put the limits of integration for calculating the background. But my question is this: Does it matter? Why do you want to know the signal to background ratio, anyway? Surely the background-subtracted peak is going to be more meaningful for just about any kind of later analysis?

-What does the original pattern look like? Is it nearly-continuous rings, or relatively isolated spots? If the latter, you can see how it performed by subtracting your background model from the original 2D image. The dark regions between spots should go to a value statistically consistent with zero. If your rings are continuous, though, this trick doesn't work. You may need to do some script programming of your own to test this.

By the way, in my experience the rotational integral is more meaningful than the rotational average (where the two differ by a factor of 2pi*r). The integral gives equal weighting to all electrons and is better, I think, from a data analysis perspective where counting statistics really matter. The integral has to be weighted by the inverse fraction of the arc contained within the original image, though, for circles that go beyond the bounds of the image.

Dear Bryan, thank you for you comments;

I checked the several diffraction images as you can seen from the images there is intensity change around 8/nm (in order to see the intensity at 8/nm brightness was adjusted). My powder samples was on the carbon film but the reign of interest was on empty space between carbon support. These images do not include intensity from carbon support. My samples becoming amorphous with e-beam and the image was taken 10-15 seconds after first beam interaction, at this time samples can be amorphized (I'm not sure). (yellow lines in the images refer to 8/nm) (original one is first image, second image is brightness adjusted, third image after amorphization, last one is for comparion of another particle)

secondly I did my experiments at different country, thats why I cannot do experiments with different parameters right now (maybe in future).

For the aligning the rotational average profile center, I did it by manually. I change the diameter of the inner ring as same with the transmitted beam diameter and placed the ring to center then calculated the intensity profile.

I am interested with the P/B ratio because as I said my samples turn into an amorphous state under e-beam with time. I take diffraction image series with time and I want to quantify the amorphization by using peak and background intensities. I want to use this ratio because experiments were did at different microscopes (one have lab6 other have FEG thats why intensities and background values changes although I use same WD, beam size, magnification, and beam current).

thats why I believed that just measuring the peak intensity does not give a meaningful data for comparison. And I am only interested with the peak about 3/nm.

Lastly I do not know rotational integral measurement can you explain it a little bit please.

Additionally any comments are welcomed.